4.7.49 \(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\)

ODE
\[ x^3 y'(x)=y(x) \left (x^2+y(x)\right ) \] ODE Classification

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00778647 (sec), leaf count = 17

\[\left \{\left \{y(x)\to \frac {x^2}{c_1 x+1}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 19

\[ \left \{ -{x}^{-2}-{\frac {{\it \_C1}}{x}}+ \left (y \relax (x ) \right ) ^{-1}=0 \right \} \] Mathematica raw input

DSolve[x^3*y'[x] == y[x]*(x^2 + y[x]),y[x],x]

Mathematica raw output

{{y[x] -> x^2/(1 + x*C[1])}}

Maple raw input

dsolve(x^3*diff(y(x),x) = y(x)*(x^2+y(x)), y(x),'implicit')

Maple raw output

-1/x^2-1/x*_C1+1/y(x) = 0